Review of 2D/3D reconstruction using statistical shape and intensity models and X-ray image synthesis: towards a unified framework

Patient-specific three-dimensional (3D) bone models are useful for a number of clinical applications such as surgery planning, postoperative evaluation as well as implant and prosthesis design. Two--dimensional--to--three--dimensional (2D/3D) reconstruction, also known as model-to-modality or atlas--based 2D/3D registration, provides a means of obtaining a 3D model of a patient's bone(s) from their 2D radiographs, when 3D imaging modalities are not available. The preferred approach to estimating both shape and density information (that would be present in a patient's CT data) for 2D/3D reconstruction makes use of digitally reconstructed radiographs and deformable models in an iterative, non-rigid, intensity-based approach. Based on a large number of state-of-the-art 2D/3D bone reconstruction methods, a unified mathematical formulation of the problem is proposed in a common conceptual framework, using unambiguous terminology. In addition, shortcomings, recent adaptations and persisting challenges are discussed along with insights for future research.